Séminaires : Séminaire d'Algèbre

In this talk, we discuss our approach to ``higher monoidal Deligne conjecture''.
An interest to this statement raised after the proof of Kontsevich formality theorem given by D.Tamarkin. In this case, it says that the cohomological Hochschild complex of any associative algebra A has a structure of a homotopical 2-algebra. The corresponding monoidal abelian category is the category of A-bimodules.
 We found a proof of a more general statement, which works for a general monoidal abelian category. We adapt the approach of Kock and Toen in their ``simplicial Deligne conjecture''. In the linear situation, we replace Segal monoids used by Kock and Toen by rather exotic objects called Leinster monoids. Rectification of Leinster monoids is one of our technical tools.
Another technical tool is the Drinfeld dg quotient and its refined version, which enjoys a nicer monoidal behaviour. If time permits, we discuss some conceptual problems towards a higher-monoidal generalisation of our results.